Transcript
ELECTROMAGNETIC WAVES
The Nature Of Electromagnetic Waves
An electromagnetic wave consists of the traveling fluctuation of both electric and magnetic fields.
Electromagnetic waves are generated near an antenna by charges moving in the antenna.
In diagram a, time = 0, there is no separation of charge, the electric field strength is zero.
In diagram b, maximum voltage has caused maximum separation of charge and maximum electric field strength in the direction shown.
In diagram c, the voltage has returned to zero as has the charge separation and the electric field strength.
In diagram d, we have maximum voltage, charge separation, and electric field strength in the opposite direction.
In diagram e, the voltage, charge separation, and electric field strength have returned to zero.
This constitutes a disturbance in the equilibrium electric field of the region which travels out in all directions as a wave.
A changing electric field causes the existence of a changing magnetic field. The magnetic field changes associated with the propagating disturbance form a right angle with the electric field changes.
Since the direction of propagation of the wave is at 90° with respect to both the electric field changes and the magnetic field changes, an electromagnetic wave is a transverse wave.
Since electric and magnetic fields exist everywhere in space(they are normally = 0 in empty space) electromagnetic waves can travel anywhere even if there is no matter to travel through.
In fact, electromagnetic waves travel fastest through a vacuum. The speed of light(electromagnetic radiation) in a vacuum is c = 3.0 x 108 m/s. In matter, the speed of light is always less.
The Electromagnetic Spectrum
The electromagnetic spectrum consists of all the frequencies of electromagnetic radiation.
The lowest frequencies are radio waves, both AM and FM. This includes TV signals. Microwaves are part of the radio signal spectrum and are sometimes used to transmit information.
The infrared region is between radio waves and visible light. Infrared is absorbed and converted to heat energy very well. It is not visible.
Visible light frequencies occupy a very small part of the complete electromagnetic spectrum. These are the frequencies we actually see. Our eyes and brain interpret different frequencies as different colors. We use ROYGBIV to help us remember the order of the colors with red being the lowest frequency sensed and violet the highest.
Ultraviolet frequencies are not visible. They are beyond violet and are used to kill bacteria, attract insects, and tan skin. They have more energy per photon than visible light.
X - rays are higher frequency than ultraviolet light and have more energy. They pass through soft tissue with a relatively low absorption rate but the higher energy content makes exposure to large amounts of them dangerous. They are useful in forming images of internal objects.
Gamma rays are higher frequency and energy than X-rays. They are produced in nuclear reactions and can cause serious damage to living tissue.
Electromagnetic radiation obeys the same relationship between frequency and wavelength as other waves. The equation relating them is:
V = f?
where V is the speed of the wave, f is its frequency and ? is its wavelength.
Example
Find the range of the wavelengths in a vacuum for visible light ranging from 4.0 x 1014 Hz to 7.9 x 1014 Hz. c = 3.0 x 108 m/s.
The Speed of Light
The speed of light was first measured accurately by Albert Michelson in 1926. His result was less than 1/100 % off.
His work confirmed the theory of Maxwell who theoretically calculated the speed of light. His equation was:
C = 1/(?0?0)½
It gave a value of 3.00 x 108 m/s.
The Doppler Effect and Electromagnetic Waves
The Doppler Effect in sound waves caused an apparent increase or decrease in the observed frequency due to the motion of the source or the observer of the sound wave.
The same effect occurs in electromagnetic waves but the equations are a little different.
In the case of sound waves, the motion of the source, observer and the medium all were considered. In the case of electromagnetic waves only the motion of the source and the observer must be considered. The simplified equation is:
f0 = fs(1 + vrel/c)
In this equation, f0 is the observed frequency, fs is the frequency emitted by the source, vrel is the magnitude of the relative velocity between the two and c is the speed of light.
Use the + sign if the observer and source are approaching each other. Use the - sign if they are moving apart.
Example
A distant galaxy emits light that has a wavelength of 434.1 nm. On Earth, the wavelength of this light is measured to be 438.6 nm. (a) Is this galaxy approaching or receding from the Earth?
(b) Find the speed of the galaxy relative to the Earth.
Polarization
Transverse waves can be polarized. This means that their displacements from equilibrium can be confined to one plane.
The example above uses a polarized mechanical wave as an example. The wave is said to be linearly polarized because the rope vibrations are all in one plane. Another term that is used is plane polarized.
The wave passes through the top slit since it is oriented in the same direction as the vibrations. The wave does not pass through the bottom slit since there is no room for vertical displacements.
Longitudinal waves cannot be polarized since the vibrations are oriented in the same direction as the direction of travel of the wave.
Unpolarized light contains light waves with random orientations of electric and magnetic field vibrations.
Polarized light can be formed from unpolarized light with the use of Polaroid film, a type of polarizing material. Components of light waves with vibrations oriented along the transmission axis of the film pass through. Those oriented at right angles do not.
Since the component of the electric field perpendicular to the axis of transmission does not pass through, the intensity of the light is reduced by ½. For unpolarized light, the polarizing material absorbs ½ of the light energy incident on it and transmits ½.
When two pieces of polarizing film are used to study light, the first piece is called the polarizer and the second is called the analyzer. The polarizer converts unpolarized light to polarized light and the analyzer can be used to control brightness or investigate optically active substances(optically active substances cause the plane of polarization to rotate as the light passes through).
The intensity of the light transmitted by the analyzer is determined by Malus's Law. It states:
S = S0cos2?
where S is the average intensity leaving the analyzer, S0 is the average intensity of light entering the analyzer, and ? is the angle between the transmission axis of the polarizer and that of the analyzer.
Example
Find the intensity of the transmitted beam when ?1 = 19°, ?2 = 55°, and ?3 = 100.0° if the initial intensity is 1260 w/m2.
Polarized light exists in nature when unpolarized light is reflected or scattered. The intensity of reflections off of horizontal surfaces is reduced by wearing sunglasses with vertically polarized lenses. Also the sky will appear different when wearing polarized sunglasses due to the elimination of horizontally polarized light.
